How to describe the electrons defined by the following quantum numbers?

n=3, l=0, #m_l=0#
n=2, l=1 #m_l=1#
Do I just have to say that it has for example one 3s orbital with 3 subshells or do I have to add other information as well? I am struggling a bit with this one. Thanks in advance.

1 Answer
Apr 10, 2018

Answer:

Here's how you can do that.

Explanation:

You have values for three our of the four quantum numbers that we use to describe the location and the spin of an electron inside an atom.

  • the principal quantum number, #n#
  • the angular momentum quantum number, #l#
  • the magnetic quantum number, #m_l#.

This means that in order to describe the electrons defined by these two incomplete quantum number sets, you must mention

  • the energy shell in which the electron is located because you know the value of #n#
  • the energy subshell in which you can find the electron because you know the value of #l#
  • the orientation of the orbital in which the electron resides because you know the value of #m_l#

For the first set, you have

#n = 3, l=0, m_l = 0#

This set describes an electron that

  • is located in the third energy shell because #n = 3#
  • is located in the #s# subshell because #l = 0#
  • is located in the #s# orbital because #m_l = 0#

So for this first electron, you have the third energy shell, the #3s# subshell, and the #3s# orbital. You don't know the value of the spin quantum number, #m_s#, so you can't specify the spin of the electron.

For the second set, you have

#n = 2, l =1, m_l = 1#

This time, the set describes an electron that

  • is located in the second energy shell because #n = 2#
  • is located in the #p# subshell because #l = 1#
  • is located in one of the three #p# orbitals because #m_l = 1#

So for this electron, you have the second energy shell, the #2p# subshell, and one of the three #2p# orbitals, let's say #2p_x#. Once again, you don't have the value of #m_s#, so you can't say anything about the spin of the electron.